A very simple example goes as follows: we can divide the set N={1,2,3,4,5,6,7,8,...} into two pieces that we can rearrange so as to form the set M={1,2,4,5,6,7,8,9,10,...}. P1 consists of all multiples of 3 and P2 consists of the rest of N. Leave P2 where it is and move P1 three units to the right, this gives us {1,2,4,5,3,7,8,6,...}, which looks just like M.
